A former producer of “The Apprentice” and others are warning that the recently leaked 2005 recording of Donald Trump having a lewd conversation about women was “just the beginning.”

“As a producer of Seasons 1 & 2 of #theapprentice I assure you: when it comes to the #trumptapes there are far worse. #justthebeginning,” Emmy–winning producer Bill Pruitt tweeted Saturday.

“The Bachelor” producer Mike Fleiss similarly wrote on Twitter: “Told ya!!! The first of The Trump Tapes has been released. Boom! A lot more where that came from! @realDonaldTrump is a pure scumbag!!!”

On Sunday, television producer Chris Nee speculated that legal fees were the reason why footage from “The Apprentice,” Mr. Trump’s former show, had not yet been made available.

“Hey @mcuban - offer to pay the legal fees and fines of anyone who produces the hot mic tapes from #TheApprentice - last few seasons will do,” Ms. Nee tweeted to billionaire Mark Cuban, Us Weekly reported.

“I don’t have the tapes. I’ve signed a Burnett contract & know leak fee is 5 mill. Hearing from producers/crew N word is the ‘much worse,’” she wrote in a now-deleted tweet.

She later added, “Folks, I have never worked on The Apprentice. I don’t know what’s out there. Or what still exists. I’ve heard rumors. Would love to know.”

The Washington Post on Friday published a 2005 tape of Mr. Trump talking with Billy Bush, then of “Access Hollywood,” about groping and having sex with women. During the private conversation, in which Mr. Trump was seemingly unaware his microphone was hot, the now-presidential candidate talked about trying to sleep with a married woman and being able to use his celebrity status to take advantage of women.

The Associated Press last week issued a report after interviewing more than 20 former crew members, editors and contestants from “The Apprentice,” who reportedly “gave concurring accounts of inappropriate conduct on the set.”

According to the AP, eight former crew members claimed that Mr. Trump repeatedly made lewd comments about a camerawoman he said had a nice rear, and compared her beauty to that of his daughter, Ivanka.

The Trump campaign issued a statement refuting the claims in the AP story.

“These outlandish, unsubstantiated and totally false claims fabricated by publicity-hungry, opportunistic, disgruntled former employees have no merit whatsoever,” Hope Hicks, Mr. Trump’s campaign spokeswoman, told the AP. “The Apprentice was one of the most successful prime-time television shows of all time and employed hundreds of people over many years, many of whom support Mr. Trump’s candidacy.”

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